TY - JOUR
T1 - Structure theorems and the dynamics of nitrogen catabolite repression in yeast
JF - Proceedings of the National Academy of Sciences of the United States of America
JO - Proc Natl Acad Sci U S A
SP - 5647
LP - 5652
DO - 10.1073/pnas.0501339102
VL - 102
IS - 16
AU - Boczko, Erik M.
AU - Cooper, Terrance G.
AU - Gedeon, Tomas
AU - Mischaikow, Konstantin
AU - Murdock, Deborah G.
AU - Pratap, Siddharth
AU - Wells, K. Sam
Y1 - 2005/04/19
UR - http://www.pnas.org/content/102/16/5647.abstract
N2 - By using current biological understanding, a conceptually simple, but mathematically complex, model is proposed for the dynamics of the gene circuit responsible for regulating nitrogen catabolite repression (NCR) in yeast. A variety of mathematical “structure” theorems are described that allow one to determine the asymptotic dynamics of complicated systems under very weak hypotheses. It is shown that these theorems apply to several subcircuits of the full NCR circuit, most importantly to the URE2–GLN3 subcircuit that is independent of the other constituents but governs the switching behavior of the full NCR circuit under changes in nitrogen source. Under hypotheses that are fully consistent with biological data, it is proven that the dynamics of this subcircuit is simple periodic behavior in synchrony with the cell cycle. Although the current mathematical structure theorems do not apply to the full NCR circuit, extensive simulations suggest that the dynamics is constrained in much the same way as that of the URE2–GLN3 subcircuit. This finding leads to the proposal that mathematicians study genetic circuits to find new geometries for which structure theorems may exist.
ER -